what is litigation?
why do interest groups choose this as a technique to get what they want?

Litigation is to take in issue to court for a trial.
There are a couple of reasons for interests groups to do this. First they get a legal opinion on a particular topic, and second they will get the attending publicity for that trial. Therefore, they will not only present their case in a court of law, but also in a court of public opinion. Both are effective in getting a particular opinion judged.